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I apologize if similar question has been already asked.

I have to compute optimal allocation of investment I between market asset and risk free asset. The investor's utility function is $U(w)=E(r_P)- γσ^2(r_P))/2$, $γ = 3$.

Then I use two formulas:

$E(r_P) = r_F + ((E(r_M) - r_F)σ_P)/σ_M$

$σ^2_P = w^2_1σ^2_1 + w^2_2σ^2_2 + 2w_1 w_2 σ_1 σ_2 ρ$

Which I plug in the utility function, before taking the derivatives wrt $w_1$ & $w_2$ . The result I obtained after equating both FOC seems wrong, because I can't use $γ = 3$ information anywhere to solve the problem:

$w_1 = ρ^2$

So where's the mistake?

Also I don't know the code for fraction line, so sorry about the messy notation.

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  • $\begingroup$ I don't see $\beta$ appear in $U(w)$? $\endgroup$ – Bob Jansen Aug 28 '19 at 13:56
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    $\begingroup$ I figured out that γ=3 and not β. $\endgroup$ – Svit Valenčič Aug 28 '19 at 17:01
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    $\begingroup$ You can either self-answer or delete the question. I don't believe anyone can give a useful answer now. $\endgroup$ – Bob Jansen Aug 28 '19 at 20:14

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